/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_biquad_cascade_df2T_f32.c
*
* Description:  Processing function for the floating-point transposed
*               direct form II Biquad cascade filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated
*
* Version 0.0.7  2010/06/10
*    Misra-C changes done
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupFilters
 */

/**
 * @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
 *
 * This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
 * The filters are implemented as a cascade of second order Biquad sections.
 * These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
 * Only floating-point data is supported.
 *
 * This function operate on blocks of input and output data and each call to the function
 * processes <code>blockSize</code> samples through the filter.
 * <code>pSrc</code> points to the array of input data and
 * <code>pDst</code> points to the array of output data.
 * Both arrays contain <code>blockSize</code> values.
 *
 * \par Algorithm
 * Each Biquad stage implements a second order filter using the difference equation:
 * <pre>
 *    y[n] = b0 * x[n] + d1
 *    d1 = b1 * x[n] + a1 * y[n] + d2
 *    d2 = b2 * x[n] + a2 * y[n]
 * </pre>
 * where d1 and d2 represent the two state values.
 *
 * \par
 * A Biquad filter using a transposed Direct Form II structure is shown below.
 * \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
 * Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
 * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
 * Pay careful attention to the sign of the feedback coefficients.
 * Some design tools flip the sign of the feedback coefficients:
 * <pre>
 *    y[n] = b0 * x[n] + d1;
 *    d1 = b1 * x[n] - a1 * y[n] + d2;
 *    d2 = b2 * x[n] - a2 * y[n];
 * </pre>
 * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
 *
 * \par
 * Higher order filters are realized as a cascade of second order sections.
 * <code>numStages</code> refers to the number of second order stages used.
 * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
 * A 9th order filter would be realized with <code>numStages=5</code> second order stages with the
 * coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
 *
 * \par
 * <code>pState</code> points to the state variable array.
 * Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.
 * The state variables are arranged in the <code>pState</code> array as:
 * <pre>
 *     {d11, d12, d21, d22, ...}
 * </pre>
 * where <code>d1x</code> refers to the state variables for the first Biquad and
 * <code>d2x</code> refers to the state variables for the second Biquad.
 * The state array has a total length of <code>2*numStages</code> values.
 * The state variables are updated after each block of data is processed; the coefficients are untouched.
 *
 * \par
 * The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
 * The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
 * That is why the Direct Form I structure supports Q15 and Q31 data types.
 * The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables <code>d1</code> and <code>d2</code>.
 * Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
 * The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.
 *
 * \par Instance Structure
 * The coefficients and state variables for a filter are stored together in an instance data structure.
 * A separate instance structure must be defined for each filter.
 * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
 *
 * \par Init Functions
 * There is also an associated initialization function.
 * The initialization function performs following operations:
 * - Sets the values of the internal structure fields.
 * - Zeros out the values in the state buffer.
 *
 * \par
 * Use of the initialization function is optional.
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 * To place an instance structure into a const data section, the instance structure must be manually initialized.
 * Set the values in the state buffer to zeros before static initialization.
 * For example, to statically initialize the instance structure use
 * <pre>
 *     arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};
 * </pre>
 * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer.
 * <code>pCoeffs</code> is the address of the coefficient buffer;
 *
 */

/**
 * @addtogroup BiquadCascadeDF2T
 * @{
 */

/**
 * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
 * @param[in]  *S        points to an instance of the filter data structure.
 * @param[in]  *pSrc     points to the block of input data.
 * @param[out] *pDst     points to the block of output data
 * @param[in]  blockSize number of samples to process.
 * @return none.
 */

void arm_biquad_cascade_df2T_f32(
    const arm_biquad_cascade_df2T_instance_f32* S,
    float32_t* pSrc,
    float32_t* pDst,
    uint32_t blockSize)
{

	float32_t* pIn = pSrc;                         /*  source pointer            */
	float32_t* pOut = pDst;                        /*  destination pointer       */
	float32_t* pState = S->pState;                 /*  State pointer             */
	float32_t* pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
	float32_t acc0;                                /*  accumulator               */
	float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
	float32_t Xn;                                  /*  temporary input           */
	float32_t d1, d2;                              /*  state variables           */
	uint32_t sample, stage = S->numStages;         /*  loop counters             */

#ifndef ARM_MATH_CM0

	float32_t Xn1, Xn2;                            /*  Input State variables     */
	float32_t acc1;                                /*  accumulator               */



	/* Run the below code for Cortex-M4 and Cortex-M3 */
	do {
		/* Reading the coefficients */
		b0 = *pCoeffs++;
		b1 = *pCoeffs++;
		b2 = *pCoeffs++;
		a1 = *pCoeffs++;
		a2 = *pCoeffs++;

		/*Reading the state values */
		d1 = pState[0];
		d2 = pState[1];

		/* Apply loop unrolling and compute 4 output values simultaneously. */
		sample = blockSize >> 2u;

		/* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
		 ** a second loop below computes the remaining 1 to 3 samples. */
		while(sample > 0u) {

			/* y[n] = b0 * x[n] + d1 */
			/* d1 = b1 * x[n] + a1 * y[n] + d2 */
			/* d2 = b2 * x[n] + a2 * y[n] */

			/* Read the first input */
			Xn1 = *pIn++;

			/* y[n] = b0 * x[n] + d1 */
			acc0 = (b0 * Xn1) + d1;

			/* d1 = b1 * x[n] + d2 */
			d1 = (b1 * Xn1) + d2;

			/* d2 = b2 * x[n] */
			d2 = (b2 * Xn1);

			/* Read the second input */
			Xn2 = *pIn++;

			/* d1 = b1 * x[n] + a1 * y[n] */
			d1 = (a1 * acc0) + d1;

			/* Store the result in the accumulator in the destination buffer. */
			*pOut++ = acc0;

			d2 = (a2 * acc0) + d2;

			/* y[n] = b0 * x[n] + d1 */
			acc1 = (b0 * Xn2) + d1;

			/* Read the third input */
			Xn1 = *pIn++;

			d1 = (b1 * Xn2) + d2;

			d2 = (b2 * Xn2);

			/* Store the result in the accumulator in the destination buffer. */
			*pOut++ = acc1;

			d1 = (a1 * acc1) + d1;

			d2 = (a2 * acc1) + d2;

			/* y[n] = b0 * x[n] + d1 */
			acc0 = (b0 * Xn1) + d1;

			d1 = (b1 * Xn1) + d2;

			d2 = (b2 * Xn1);

			/* Read the fourth input */
			Xn2 = *pIn++;

			d1 = (a1 * acc0) + d1;

			/* Store the result in the accumulator in the destination buffer. */
			*pOut++ = acc0;

			d2 = (a2 * acc0) + d2;

			/* y[n] = b0 * x[n] + d1 */
			acc1 = (b0 * Xn2) + d1;

			d1 = (b1 * Xn2) + d2;

			d2 = (b2 * Xn2);

			/* Store the result in the accumulator in the destination buffer. */
			*pOut++ = acc1;

			d1 = (a1 * acc1) + d1;

			d2 = (a2 * acc1) + d2;

			/* decrement the loop counter */
			sample--;

		}

		/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
		 ** No loop unrolling is used. */
		sample = blockSize & 0x3u;

		while(sample > 0u) {
			/* Read the input */
			Xn = *pIn++;

			/* y[n] = b0 * x[n] + d1 */
			acc0 = (b0 * Xn) + d1;

			/* Store the result in the accumulator in the destination buffer. */
			*pOut++ = acc0;

			/* Every time after the output is computed state should be updated. */
			/* d1 = b1 * x[n] + a1 * y[n] + d2 */
			d1 = ((b1 * Xn) + (a1 * acc0)) + d2;

			/* d2 = b2 * x[n] + a2 * y[n] */
			d2 = (b2 * Xn) + (a2 * acc0);

			/* decrement the loop counter */
			sample--;
		}

		/* Store the updated state variables back into the state array */
		*pState++ = d1;
		*pState++ = d2;

		/* The current stage input is given as the output to the next stage */
		pIn = pDst;

		/*Reset the output working pointer */
		pOut = pDst;

		/* decrement the loop counter */
		stage--;

	} while(stage > 0u);

#else

	/* Run the below code for Cortex-M0 */

	do {
		/* Reading the coefficients */
		b0 = *pCoeffs++;
		b1 = *pCoeffs++;
		b2 = *pCoeffs++;
		a1 = *pCoeffs++;
		a2 = *pCoeffs++;

		/*Reading the state values */
		d1 = pState[0];
		d2 = pState[1];


		sample = blockSize;

		while(sample > 0u) {
			/* Read the input */
			Xn = *pIn++;

			/* y[n] = b0 * x[n] + d1 */
			acc0 = (b0 * Xn) + d1;

			/* Store the result in the accumulator in the destination buffer. */
			*pOut++ = acc0;

			/* Every time after the output is computed state should be updated. */
			/* d1 = b1 * x[n] + a1 * y[n] + d2 */
			d1 = ((b1 * Xn) + (a1 * acc0)) + d2;

			/* d2 = b2 * x[n] + a2 * y[n] */
			d2 = (b2 * Xn) + (a2 * acc0);

			/* decrement the loop counter */
			sample--;
		}

		/* Store the updated state variables back into the state array */
		*pState++ = d1;
		*pState++ = d2;

		/* The current stage input is given as the output to the next stage */
		pIn = pDst;

		/*Reset the output working pointer */
		pOut = pDst;

		/* decrement the loop counter */
		stage--;

	} while(stage > 0u);

#endif /*  #ifndef ARM_MATH_CM0         */

}


/**
 * @} end of BiquadCascadeDF2T group
 */
